A soccer player stops a ball that is moving across a field. Her foot is in contact with the ball for 0.3 s, during which time the ball's average acceleration is 12 m/s2. What was the ball's initial velocity?
V/t = acceleration
V = 12 ms^-2 * 0.3 s = 3.6 m/s
To find the ball's initial velocity, we can use the equation:
v = u + at
where:
v = final velocity (which is 0, as the ball stops)
u = initial velocity (what we want to find)
a = acceleration (given as 12 m/s^2)
t = time (given as 0.3 s)
Plugging in the values into the equation, we get:
0 = u + (12 m/s^2) * (0.3 s)
Simplifying the equation:
0 = u + 3.6 m/s
Rearranging the equation to solve for u:
u = -3.6 m/s
Therefore, the ball's initial velocity was -3.6 m/s. The negative sign indicates that the ball was moving in the opposite direction of the player's foot when it was stopped.
To find the ball's initial velocity, we need to use the equation of motion:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
In this case, we know the following values:
v = ?
u = initial velocity (to be determined)
a = 12 m/s^2
t = 0.3 s
Since the question asks for the ball's initial velocity, we can rearrange the equation as follows:
u = v - at
Since the ball stops, its final velocity (v) is 0 m/s. Therefore, we can substitute this value into the equation:
u = 0 - (12 m/s^2)(0.3 s)
Calculating this, we get:
u = -3.6 m/s
The negative sign indicates that the initial velocity is in the opposite direction of its final velocity, which in this case is stopping. Therefore, the ball's initial velocity was -3.6 m/s.